Learning mixtures of arbitrary gaussians
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
A Two-Round Variant of EM for Gaussian Mixtures
UAI '00 Proceedings of the 16th Conference on Uncertainty in Artificial Intelligence
Learning Mixtures of Gaussians
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
A spectral algorithm for learning mixture models
Journal of Computer and System Sciences - Special issue on FOCS 2002
On spectral learning of mixtures of distributions
COLT'05 Proceedings of the 18th annual conference on Learning Theory
Hierarchical mixture models: a probabilistic analysis
Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining
A rigorous analysis of population stratification with limited data
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
A discriminative framework for clustering via similarity functions
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Multiple Pass Streaming Algorithms for Learning Mixtures of Distributions in ${\mathbb R}^d$
ALT '07 Proceedings of the 18th international conference on Algorithmic Learning Theory
Clustering with Interactive Feedback
ALT '08 Proceedings of the 19th international conference on Algorithmic Learning Theory
Robust PCA and clustering in noisy mixtures
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Multiple pass streaming algorithms for learning mixtures of distributions in Rd
Theoretical Computer Science
Foundations and Trends® in Theoretical Computer Science
Separating populations with wide data: a spectral analysis
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Spectral methods for matrices and tensors
Proceedings of the forty-second ACM symposium on Theory of computing
Learning mixtures of arbitrary distributions over large discrete domains
Proceedings of the 5th conference on Innovations in theoretical computer science
| Hi-index | 0.00 |
We consider the problem of learning mixtures of arbitrary symmetric distributions.We formulate sufficient separation conditions and present a learning algorithm with provable guarantees for mixtures of distributions that satisfy these separation conditions. Our bounds are independent of the variances of the distributions; to the best of our knowledge, there were no previous algorithms knownwith provable learning guarantees for distributions having infinite variance and/or expectation. For Gaussians and log-concave distributions, our results match the best known sufficient separation conditions [1, 15]. Our algorithm requires a sample of size o(dk), where d is the number of dimensions and k is the number of distributions in the mixture.Wealso show that for isotropic power-laws, exponential, and Gaussian distributions, our separation condition is optimal up to a constant factor.